The x-coordinate of the given equation is x=4.
What essentially is an equation?An equation is a mathematical statement composed of two representations joined by an equal sign.An example of an equation is 3x - 5 = 16.After solving this equation, we obtain the value for the variable x as x = 7.
So,
Given:
y-3 = x ...(1)y/x²-9 = 1 ...(2)Then,
y = x+3Substitute y=x+3 in equation (2):
y/x²-9 = 1 x+3/x²-9 = 1 x+3/x²-3² = 1 1/x-3=1(Cross multiply)
x-3=1x=1+3x=4Therefore, the x-coordinate of the given equation is x=4.
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A drawing has a scale of 1:30 On the drawing, a kitchen is a rectangle measuring 12 cm by 27 cm A bedroom has an actual area of 300 000 cm² Which has the bigger actual area, the kitchen or the bedroom? You must show your working.
The actual area of the bedroom is bigger than the actual area of the kitchen.
The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The area of a rectangle is determined by its dimensions. A rectangle's area is essentially equal to the product of its length and breadth.
In the drawing, the kitchen is in the shape of a rectangle with dimensions of 12 cm × 27 cm.
Therefore, the area of the rectangle will be:
Area = Length × Breadth
Area = 12 cm × 27 cm
Area = 324 cm²
Now, the actual area of the bedroom is 300,000 cm².
Then the difference between the area,
difference = bedroom - kitchen
difference = 300,000 - 324 cm²
difference = 299676 cm²
Therefore, the area of the bedroom is bigger than the area of the kitchen.
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If AABC AFDE, which of the following statements is true? O ZA ZE O
If ∆ABC and ∆FDE are congruent, then the correct statement among options is ∠C ≅ ∠E.
Congruent figures refers to the figures that can be superimposed on each other. This states that the angles and sides are similar for both the figures being compared. We are given that two triangles are congruent. Same will be true for their sides as well.
Thus, we can interpret that similar angles in the mentioned two triangles will be -
∠A ≅ ∠F
∠B ≅ ∠D
∠C ≅ ∠E
Similarly, the similar sides for both triangles will be -
AB ≅ FD
BC ≅ DE
AC ≅ FE
Therefore, in the congruent triangles ABC and FDE, ∠C and ∠E are congruent.
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Hayley and Phoebe have a lemonade stand where they sell cups of lemonade for $0.75 a piece. The function p(c)=0.75c represents the profit p(c) that the girls
earn if they sell c cups of lemonade. The girls have 150 cups.
Find the domain and range. Write your answers as compound inequalities.
The domain of the function is given by: 0 ≤ c ≤ 150
The range of the function is given by : 0 ≤ p(c) ≤ 112.5
The range of values that we are permitted to enter into our function is known as the domain of a function.
The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of domain values.In order to identify the values of the independent variable x and acquire the domain, we simply solve the equation y = f(x). Simply put, x=g(y) will calculate the function's range after we identify g's domain (y).The given statement states that the profit from selling 150 cups of lemonade is denoted by p(c) such that p(c) = 0.75c
Now the girls can sell a maximum of 150 lemonades.
Hence the domain of the values are : 0 ≤ c ≤ 150
at x=0 , p(c) = 0.75 × 0 = 0
at x= 150 , p(c) = 0.75 × 150 = 112.50
Therefore the range of the function is : 0 ≤ p(c) ≤ 112.5
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TIME REMAINING
01:47:26
Every year, the US Census Bureau publishes its Annual Survey of School System Finances. The back-to-back stemplot below shows the 2016 per-pupil expenditure (rounded to the nearest $100) for eastern and western states and the District of Columbia in the United States.
A stemplot titled Per-pupil expenditure for U S States. 7 line 0 means 7,000 dollars per pupil. Eastern States: The values are 87, 88, 88, 89, 92, 98, 92, 92, 102, 113, 114, 117, 121, 132, 141, 142, 147, 153, 154, 155, 156, 179, 184, 190, 191, 223. Western States: The values are 70, 71, 76, 81, 90, 91, 92, 96, 97, 98, 100, 103, 105, 105, 108, 110, 112, 113, 115, 123, 123, 134, 138, 164, 175.
Based on the stemplot, which of the following is a correct comparison of the eastern and western states’ expenditures?
The stemplot gives a correct comparison of eastern and western states’ expenditures as The eastern states have, on average, a higher per-pupil expenditure than the western states.
What does the stemplot show?The Eastern States have expenditure per pupil which are higher in number and in quantity. For instance, they have per-pupil expenditure of $153, $154, $155, and $156. They also have $191, and $190.
When compared to the western states therefore, the eastern states seem to on average, spend more per-pupil.
Options for this question include:
The western states exhibit more variability in their expenditures than the eastern states. The eastern states have, on average, a higher per-pupil expenditure than the western states. The distribution of per-pupil expenditures in the eastern states is more symmetric than the distribution of the western states. The distribution of the western states' per-pupil expenditure is skewed left, while the distribution of the eastern states' per-pupil expenditure is skewed right. Valid conclusions comparing the distributions cannot be made, since there is a different number of states in each group.Find out more on stemplots at https://brainly.com/question/11320163
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How do I solve 3/4m - 1/12m = 7/8?? (This is a linear equation problem btw if you didn’t know).
Evaluate 32+ (6-2) 4-3. (1 point)
The simplified form of the given expression is 45.
The given expression is 32+(6-2)4-3.
An expression in math is a sentence that contains at least two numbers/variables and at least one math operation. The mathematics operators will be addition, subtraction, multiplication and division.
The expression is 32+(6-2)4-3.
Firstly, we will simplify the subtraction which is in the bracket, we get
32+(6-2)4-3=32+(4)4-3
Now, we will simplify the multiplication, we get
32+(6-2)4-3=32+16-3
Further, we will simplify the addition, we get
32+(6-2)4-3=48-3
Furthermore, we will simplify the subtraction, we get
32+(6-2)4-3=45
Hence, the simplified form of the given expression 32+(6-2)4-3 is 45.
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Jalen is computing the slope of a line on the graph below. Which statement describes Jalens error?
Jalen computed the raitio in e to change in y
Jalen use the ordered pairs in the wrong order
Jalen made a computational error
Jalen used an ordered pair that is not on the line
The statement which describes Jalen's error is that: A. Jalen computed the ratio of change in x to change in y.
What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
How to calculate the slope of a line?Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Slope, m = Δy/Δx
In this context, we can reasonably infer and logically deduce that the statement which describes Jalen's error is that Jalen computed the ratio of change in x to change in y i.e Δx/Δy, instead of Δy/Δx = (0 - 3)/(-4 - 2).
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Which number is ninetythree and six hundredths
Answer: 93/600 or 93.06
Step-by-step explanation:
6b + 3x = 12
2b - 2x = 4 pls help i need this answer asap
Normal curve g has a mean of 50 and a standard deviation of 5. Normal curve h has a mean of 50 and a standard deviation of 10. How do the shapes of these two normal curves compare if they are drawn using the same scale?.
Drawn using the same scale, the shape of the normal curve H will be more spread out than the shape of the normal curve G.
Normal curve, or Gaussian distribution, is a curve that describes data form a variable that has infinite, or very large, number of possible values distributed among the population. It has a symmetric shape, and the distribution rises in the middle, and goes down to the left and to the right. The mean is equal to the mode and median and is located at the middle or top of the curve.
If two normal curves have the same mean, but different standard deviations, then the curve with the larger standard deviation will have a more spread out shape than the other.
If Normal curve H has a standard deviation of 10 and normal curve G has 5, but both has the same mean, then Normal curve H has a more spread out shape than the curve of normal curve G.
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$10 off $50
Buy-1-Get-1 Half Off
Customers
Spending
More than $30
Customers
Spending
$30 or Less
Which statement best describes how the manager can check if there is an association between the two variables?
The manager must check relative frequencies by row because there are more than two different promotions.
The manager must check relative frequencies by column because there are more than two different promotions
The manager cannot use relative frequencies to look for an association because there are more than two differes
s by now and by column to look for an association.
There are more than two distinct promotions, thus the manager must verify the relative frequencies per column.
The management must examine the relative frequencies by column since there are more than two different promotions, according to the statement that best sums up the relationship between the two variables.
Relative frequency is defined.The ratio of the number of times an event happened to the overall number of events is known as the relative frequency. In essence, it is the frequency ratio between the subgroups and the entire population.
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Help please let me know if you get it
The line passing through point [tex]F[/tex] that is skew to [tex]\overleftrightarrow{EH}[/tex] is [tex]\overleftrightarrow{CF}[/tex] .
Skew lines are two parallel but non-intersecting lines. The two lines that pass through the opposing edges of a normal tetrahedron are a straightforward illustration of a pair of skew lines.
To check if two lines are skew we need to check by following the steps mentioned below:
Step 1: Find lines that do not cross one another.
Step 2: Verify that these line pairs are not also parallel to one another.
Step 3: Check whether these non-intersecting, non-parallel lines are non-coplanar. If the answer is affirmative, the selected pair of lines are skew.
Therefore, the line [tex]\overleftrightarrow{CF}[/tex] passes through point F, the line is not parallel to the line [tex]\overleftrightarrow{EH}[/tex] and is also non-coplanar. Both the lines do not intersect each other.
Hence, [tex]\overleftrightarrow{CF}[/tex] and [tex]\overleftrightarrow{EH}[/tex] are skew lines.
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What is the quotient of (−192) ÷ (−16) ÷ (−4)?
a contractor buys 8.2 square feet of sheet metal. she used 2.1 square feet so far and has $183 worth of sheet metal remaining. write and solve an equation to find out how much sheet metal costs per foot
1) The equation that shows the cost of sheet metal per foot, s/ft² = $183 ÷ 6.1 ft².
2) The solution of the equation shows that sheet metal costs $30 per foot.
What is an equation?An equation is a mathematical expression that states that two variables are equal.
Equations are stated using the equation symbol (=).
Data and Calculations:The total quantity of sheet metal bought = 8.2 ft²
The total quantity of sheet metal used = 2.1 ft²
The remaining quantity of sheet metal = 6.1 ft² (8.2 ft² - 2.1 ft²)
The value of the remaining quantity of sheet metal = $183
The cost of sheet metal per foot = $30 ($183/6.1 ft²) or ($183 ÷ 6.1 ft²)
Thus, the cost of sheet metal is $30 per foot.
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What are the coordinates of the midpoint of,
PQ for P(-12, 6) and Q(1,-8)?
1/4x-2=2x-9
find value for x
Answer:
Add 2 to both sides.
1/4x=2x-7
Multiply both sides by 4
x=8x-28
-8x from each side.
-7x=-28
divide both sides by -7
X=4
Answer: x=4
1. Multiply both sides by 4 to get rid of the denominator, which gives you x-8 = 8x-36
2. Subtract 8x from both sides, which gives you x - 8 - 8x= -36
3. Add 8 to both sides, which gives you x - 8x = -36 + 8
4. Simplify, -7x = -28
5. Divide both sides by -7, x = -28/-7
6. the negative signs cancel and you just get 4
There are about 61,000 people at a soccer game. How can 61,000 be written using a power of 10?
A.
Mary deposits her paycheck into her checking account every month, pays all her bills, and then puts $200 into her
money market account. She has done this for two years and now has $4,000 in a money market account that she has
not needed for expenses. Her bank requires a $250 [ninimum for regular savings accounts, $1,000 for CDs, and $1,250
for money market accounts. What would be the best option for her?
O She should do nothing; she never knows when a big expense might come up.
She should open a one-year CD with $1,000 from her money market account.
She should open a two-year CD with $2,000 from her money market account.
O She should open a regular account at another bank to keep her money safer.
Answer:
she should open a regular account to keep her money safer
Step-by-step explanation:
3. What is the GCF of 12a³ and 24a5?
A. 3a³
B. 3a5
C. 12a³
D. 12a5
Answer:
C
Step-by-step explanation:
12a³ and 24[tex]a^{5}[/tex]
the GCF of 12 and 24 is 12
the GCF of a³ and [tex]a^{5}[/tex] is a³
the GCF of both is 12a³
Graph the inequality. z is less than or equal to 5
FINE THEN 90 POINT TO WHO ANSWERS
Answer:
Lucia is using 7000 calories per minute
Step-by-step explanation:
1 kcal per hour = 1000 cal per hour = 1000/60 cal per minute
420 kilocalories = 420000 calories
Lucia is using 420000 calories per hour
Lucia is using 420000/60 calories per minute
Lucia is using 7000 calories per minute
Answer:
7000 cal per minute
Step-by-step explanation:
Express the product (5/2x+1) and (1/2x+1/4) as a trinomial in simplest form
The product of the given expressions is expressed as a trinomial as: 5/4x² + 9/8x + 1/4.
How to Solve Trinomials?Given the expressions, (5/2x +1) and (1/2x + 1/4), find the product by multiplying both together as shown below:
(5/2x + 1)(1/2x + 1/4)
Distribute
5/2x(1/2x + 1/4) + 1(1/2x + 1/4)
5/4x² + 5/8x + 1/2x + 1/4
Combine like terms
5/4x² + 9/8x + 1/4
Therefore, the product of the given expressions is expressed as a trinomial as: 5/4x² + 9/8x + 1/4.
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Write each expression as a single logarithm.
log 5-k log 2
The expression log 5-k log 2 can be expressed as log (5/[tex]2^{k}[/tex]) in the form of single logarithm.
Given that the expression is log 5-k log 2.
We are required to find the expression as a single logarithm.
Division of logarithm says that log (m/n)=log m-log n.
The expression is log 5-k log 2.
log 5-k log 2=log 5-log [tex]2^{k}[/tex]
(We have to write the power of 2 which is k because it is in front of 2)
=log (5/[tex]2^{k}[/tex])
Hence the expression log 5-k log 2 can be expressed as log (5/[tex]2^{k}[/tex]) in the form of single logarithm.
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Montserrat can make 4 bracelets in 2 1/4 hours. How many bracelets can she make per hour
Answer: Montserrat bracelets can she make per hour = 0.5625 hours
Step-by-step explanation:
Given data,
Montserrat can make 4 bracelets in 2 1/4 hours.
Let assume Montserrat can make 1 bracelets in x hours.
So,
we can write,
4 ⇒ 2 1/4
1 ⇒ x
Then,
4x = 1 * 2 1/4
4x =1* 9/4
4x = 9/4
x = (9/4)/4
x = 9/16
x = 0.5625 hours.
Therefore,
Montserrat bracelets can she make per hour = 0.5625 hours
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The cost to rent an apartment is proportional to the number of square feet in the apartment. An 800 square foot apartment costs $600 per month. What equation represents the relationship between area, A, and cost, C?
The relationship between area and cost is 3/4 means 4 times area gets 3 times cost.
Given the cost to rent an apartment is proportional to the number of square feet in the apartment.
Given the cost of an 800 sqft apartment per month = 600$
By using the given information we can define the relationship between area and cost as below
For 800 sqft = 600 $
for 1 sqft = x
It can be written as
800/1 = 600/x
By cross multiplicating the terms on both sides we get
800 * x = 600
x = 600/800
x = 3/4
The relationship between area and cost is 3/4 means 4 times area gets 3 times cost.
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What is the constant of 2x+3y+4z+5a+6b
Constants values in the expression 2x+3y+4z+5a+6b are 2,3,4 ,5 and 6.
A constant is a value or number that is consistently the same regardless of how it is expressed. For instance, in the aforementioned figure, where its face value is 36 and 82 respectively, 36 and 82 remain constant. Its worth remains constant.
To broaden our definition, we can say that a constant is something that never changes. Either a single digit or a symbol that denotes a specific number is used. You could substitute a letter like a, b, or c for a constant.
An illustration of a constant term is the mathematical symbol Pi. The word "Pi" refers to a well-known number that can be used alone.
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I need help understanding the question is x+1=-5
Answer:so you have to get x by itself so minus 1 to both sides that would equals x=-6 thats your answer but if it was 2x=-6 then you wound divide until you get x by itself hope this helps but the answer is
x=-6
Step-by-step explanation:
Answer:
I got you!
So x is basically a placeholder for a number. We don't know what that number is, so we just put the letter x so we can make an equation. x can also be shown as a ? or any symbol as long as it consitant throughout the whole equation. for x+1=-5, we are trying to find what number when added to 1 equals -5. Or.... 1+?=-5. We can subtract 1 from each side of the equation to get ?=-6. Or in this case, X=-6!
Write log 150 as a sum or difference of two logarithms. Simplify if possible.
log 150 = log 50 + log 3
∴ log 150 = 2.176
As the base is not mentioned, we will take the base as 10. We will apply the product rule of logarithms to this equation.
log (150) can also be written as log (50×3).
Therefore, log (150) = log 50 + log 3
We know, log 3 = 0.477log 150 = log 50 + 0.477
Now, we can write log 50 as log (100/2). We will use the quotient rule of logarithms.log 50 = log 100 - log 2
We know, log 100 = 2 and log 2 = 0.301∴ log 50 = 2 - 0.301
log 50 = 1.699 Substituting the value of log 50 = 1.699 in the main equation, log 150 = log 50 + log 3log 150 = 1.699 + 0.477log 150 = 2.176
Therefore, the final answer to the question log 150 = 2.176
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A figure has two pairs of parallel sides and four right angles. The figure is translated 4 units down. How many parallel sides does the imagine have?
The number of parallel sides that the translated figure will have is 2 pairs of parallel sides.
What is the result of translation of an Object?
We are given the properties of the figure as;
Number of Parallel sides = Two Pairs
Number of Right Angles = 4
Now, a rectangle is the figure that has two pairs of opposite sides parallel, and four right angles. A square could also have this same properties.
Now, if the figure is translated by 4 units down, according to transformation, that does not change the dimension of the figure and as such it retains same number of parallel sides.
Thus, the number of parallel sides that the translated figure will have is 2 pairs of parallel sides.
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Which expression is equivalent to -a times -b?
O a(-b)
O b-a
O (-a)(-b)
O a+b
Answer:
(-a)(-b)
-a ×-b
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